Hjem

I Numbers and Functions.-
1. Integers, rational numbers and real numbers.-
2. Inequalities.-
3. Functions.-
4. Powers.- II Graphs and Curves.- l. Coordinates.-
2. Graphs.-
3. The straight line.-
4. Distance between two points.-
5. Curves and equations.-
6. The circle.-
7. The parabola. Changes of coordinates.-
8. The hyperbola.- III The Derivative.- l. The slope of a curve.-
2. The derivative.-
3. Limits.-
4. Powers.-
5. Sums, products, and quotients.-
6. The chain rule.-
7. Rate of change.- IV Sine and Cosine.- l. The sine and cosine functions.-
2. The graphs.-
3. Addition formula.-
4. The derivatives.-
5. Two basic limits.- V The Mean Value Theorem.-
1. The maximum and minimum theorem.-
2. Existence of maxima and minima.-
3. The mean value theorem.-
4. Increasing and decreasing functions.- VI Sketching Curves.-
1. Behavior as x becomes very large.-
2. Curve sketching.-
3. Pol ar coordinates.-
4. Parametric curves.- VII Inverse Functions.-
1. Definition of inverse functions.-
2. Derivative of inverse functions.-
3. The arcsine.-
4. The arctangent.- VIII Exponents and Logarithms.-
1. The logarithm.-
2. The exponential function.-
3. The general exponential function.-
4. Order of magnitude.-
5. Some applications.- IX Integration.-
1. The indefinite integral.-
2. Continuous functions.-
3. Area.-
4. Upper and lower sums.-
5. The fundamental theorem.-
6. The basic properties.- X Properties of the Integral.-
1. Further connection with the derivative.-
2. Sums.-
3. Inequalities.-
4. Improper integrals.- XI Techniques of Integration.-
1. Substitution.-
2. Integration by parts.-
3. Trigonometric integrals.-
4. Partial fractions.- XII Some Substantial Exercises.-
1. An estimate for (n!)1/n.-
2. Stirling's formula.-
3. Wallis' product.- XIII Applications of Integration.-
1.Length of curves.-
2. Area in polar coordinates.-
3. Volumes of revolution.-
4. Work.-
5. Moments.- XIV Taylor's Formula.-
1. Taylor's formula.-
2. Estimate for the remainder.-
3. Trigonometric functions.-
4. Exponential function.-
5. Logarithm.-
6. The arctangent.-
7. The binomial expansion.- XV Series.-
1. Convergent series.-
2. Series with positive terms.-
3. The integral test.-
4. Absolute convergence.-
5. Power series.-
6. Differentiation and integration of power series.- Appendix
1. ? and ?.-
1. Least upper bound.-
2. Limits.-
3. Points of accumulation.-
4. Continuous functions.- Appendix
2. Physics and Mathematics.- Answers.- Supplementary Exercises.